Transfer ffffffffffffff3f from hexadecimal in binary number system

This transfer is possible in two ways: direct transfer and using the decimal system.

first, let\'s make a direct transfer.

let\'s do a direct translation from hexadecimal to binary like this:

ffffffffffffff3f₁₆ = f f f f f f f f f f f f f f 3 f = f_(=1111) f_(=1111) f_(=1111) f_(=1111) f_(=1111) f_(=1111) f_(=1111) f_(=1111) f_(=1111) f_(=1111) f_(=1111) f_(=1111) f_(=1111) f_(=1111) 3_(=0011) f_(=1111) = 1111111111111111111111111111111111111111111111111111111100111111₂

the Final answer: ffffffffffffff3f₁₆ = 1111111111111111111111111111111111111111111111111111111100111111₂

now let\'s make the transfer using the decimal system.

let\'s translate to decimal like this:

15∙16¹⁵+15∙16¹⁴+15∙16¹³+15∙16¹²+15∙16¹¹+15∙16¹⁰+15∙16⁹+15∙16⁸+15∙16⁷+15∙16⁶+15∙16⁵+15∙16⁴+15∙16³+15∙16²+3∙16¹+15∙16⁰ = 15∙1152921504606846976+15∙72057594037927936+15∙4503599627370496+15∙281474976710656+15∙17592186044416+15∙1099511627776+15∙68719476736+15∙4294967296+15∙268435456+15∙16777216+15∙1048576+15∙65536+15∙4096+15∙256+3∙16+15∙1 = 1.7293822569103E+19+1080863910568919040+67553994410557440+4222124650659840+263882790666240+16492674416640+1030792151040+64424509440+4026531840+251658240+15728640+983040+61440+3840+48+15 = 1.844674407371E+19₁₀

got It: ffffffffffffff3f₁₆ =1.844674407371E+19₁₀

Translate the number 1.844674407371E+19₁₀ в binary like this:

the Integer part of the number is divided by the base of the new number system:

1.844674407371E+19	2
0	0
0

the result of the conversion was:

1.844674407371E+19₁₀ = 00₂

the Final answer: ffffffffffffff3f₁₆ = 00₂